A description of the liquid-crystalline phase of rodlike polymers at high shear rates

Abstract

The highly nonlinear behavior of the nematic phase of rodlike polymers in shear flow is analyzed by reducing the problem to its two-dimensional analogue. Explicit solutions for the orientational distribution function are found for those situations where a stationary solution in fact exists, i.e., for the nontumbling case. The corresponding stresses are also calculated. It is found that, in a range of shear rates, the normal stress difference is negative. More generally, a very good qualitative agreement is found between theory and experiment.

Non-equilibrium nature of two-dimensional isotropic and nematic coexistence in amyloid fibrils at liquid interfaces

“…Of particular interest is the self-organization of macromolecules with a high aspect ratio into LC assemblies at interfaces, which has been treated theoretically [4][5][6] but less frequently shown experimentally 7,8 . In contrast to the 3D case and under the assumption of thermodynamic equilibrium, the 2D IN transition can be of first 4 , second order 5 , or of the Kosterlitz-Thouless continuous type leading to quasi-long-range order [9][10][11] , depending on the interactions between particles 12 and their rigidity 10 . Theoretical evidence for a truly 2D second-order transition is based on mean-field assumptions, and therefore does not account for fluctuations, which can be responsible for the suppression of long-range nematic order.…”

Influence of Electric Fields and Boundary Conditions on the Flow Properties of Nematic-Filled Cells and Capillaries

“…On the other hand, Marrucci et al (Marrucci G. and Maffettone 1989) have solved a two dimensional version of the Doi model for nematics (Doi M. and Edwards S.. F. 1986), in which the molecules are assumed to lie in the plane perpendicular to the vorticity axis, that is, in the plane parallel to both, the direction of the velocity and the direction of the velocity gradient. Despite this simplification, the predicted range of shear rates over which N is negative, is in excellent agreement with observations.…”

Analysis of 1 + 1 Dimensional Stochastic Models of Liquid Crystal Polymer Flows

“…The analysis and computation of complex fluids, i.e., non-Newtonian fluids, have attracted much attention in recent years, see, e.g., [29,30,12,23,8,9,16,17,24,34,4,5,20,25]. Mathematically speaking, the dynamics of a polymer-solvent system may be modeled by a Navier-Stokes-like equation…”

“…Many interesting dynamics were found for the shear flow in [11,25,19,20] via spherical harmonic function expansion and stochastic simulations. But simulation results in more general cases haven't come out yet for its large scale computations.…”